Australians have long valued our security alliance with the U.S., a relationship that dates back to World War II. We have been America’s most reliable friend, the only country to have fought at its side in every major conflict of the 20th and 21st centuries. Now new polling suggests Donald Trump may be tarnishing that relationship.

The first contact between President Trump and Australia’s Prime Minister Malcolm Turnbull didn’t go well. In January the president reportedly cut short a “hostile and charged” phone call, which he later described as “the worst call so far.”

The damage was repaired somewhat when the two leaders met in New York in early May. Then last week video emerged from an off-the-record charity dinner showing Mr. Turnbull poking fun at Mr. Trump. As Mr. Trump isn’t known for his self-deprecating sense of humor, the next phone call between the two leaders will no doubt be awkward.

Many Australians will have seen the humor in Mr. Turnbull’s performance. Lowy Institute polling conducted in the lead up to the 2016 election found that 77% of Australians would have preferred it if Hillary Clinton had won. Only 11% preferred Donald Trump.

Now that Mr. Trump has become president, the 2017 Lowy Institute Poll finds that 60% of Australians say Mr. Trump causes them to have an unfavorable opinion of the U.S. He’s particularly unpopular among young adults—with 70% saying he is a negative factor in their opinion of the U.S.—and women, 68% of whom disapprove of the U.S. leader.

There has also been a steep drop in Australians’ trust of the U.S.: the number who trust America “a great deal” to act responsibly in the world has halved, to 20% from 40%, since the Lowy Institute last polled this question in 2011. The 61% of Australians who trust the U.S. overall contrasts with the 90% who trust the U.K., 86% who trust Germany and 86% who trust Japan.

The number of Australians who see the U.S. as Australia’s “best friend in the world” has also halved, to 17%, from 35% in 2014. Whereas three years ago America shared the top slot on the “best friend” list alongside New Zealand, it has now dropped to second place, far behind New Zealand and tied with the U.K.

There were strong indications before the 2016 U.S. election that Australians might shun the U.S. alliance under a Trump presidency. Nearly half the Australian population, 45%, said in 2016 Lowy Institute polling that “Australia should distance itself from the United States if it elects a president like Donald Trump.”

The good news out of the 2017 poll is that Australians are able to separate the Australia-U.S. alliance from the person of Mr. Trump. For the moment, support for the alliance is holding up, and in fact has rebounded after a significant nine-point drop recorded in March 2016 polling during the U.S. presidential primary season.

More than three-quarters of Australians, 77%, still say the alliance is either “very” or “fairly” important for Australia’s security. Their overall warmth toward the U.S., as measured on the poll’s “thermometer of feelings” toward nations, has stabilized after its record five-point drop last year. Only 29% of Australians now think “Australia should distance itself from the United States under President Donald Trump.”

These results probably reflect the pragmatism for which Australians are famous. But it’s an open question how long the relationship can prosper under the weight of Mr. Trump’s behavior.

Mr. Trump has professed his skepticism about alliances, hostility to free trade and partiality to strongmen. Since taking office he has withdrawn from the Trans-Pacific Partnership, undermining perceptions of American reliability and undercutting America’s position in Asia.

Mr. Trump has also refused to endorse the principle of collective defense, which is enshrined in Article 5 of the NATO Treaty and forms the basis of all U.S. alliances. He has been careless with intelligence provided by allies. His most recent move—withdrawing from the Paris climate agreement—will likely further spook Australians, whose concern about climate change has risen in the last few years and who supported a strong commitment to the Paris accord in 2015.

No one likes being taken for granted, not even the oldest and easiest of friends. The 2017 Lowy Institute Poll reveals that fewer Australians than ever see the U.S. as our “best friend.” That should be a warning for all of us who support this alliance.